PPP surveyed 24 Congressional districts currently held by Republicans. They asked voters to choose between their current representative and a generic Democrat (data as PDF). Here are the margins they got, plotted against last November’s election result:

His conclusion:

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If the election were held today, Democrats would pick up around 30 seats, giving them control of the chamber. I do not expect this to happen. Many things will happen in the coming 12 months, and the current crisis might be a distant memory. But at this point I do expect Democrats to pick up seats next year, an exception to the midterm rule.

And it gets worse for the GOP:

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Note that in these calculations I did not even include the worst of the news for Republicans. In a followup series of questions, PPP then told respondents that their representative voted for the shutdown. At that point, the average swing moved a further 3.1% toward Democrats, and 22 out of 24 points were in the gray zone. That would be more like a 50-seat gain for Democrats – equivalent to a wave election.

I don't know if it matters. They've gerrymandered the country into control of the House. By popular vote, they would have lost the House in the last election, but popular vote doesn't count. I'm beginning to wonder if a parliamentary system wouldn't be more democratic; Representation based on percentage of vote.